The most common method by which files are transferred on the Internet is the client-server model. A central server sends the entire file to each client that requests it. The clients only speak to the server, and not to each other. The main advantages of this method are that it's simple to set up, and the files are usually always available since the servers tend to be dedicated to the task of serving, and therefore are always on and connected to the Internet.
Another method of transferring files utilizes a peer-to-peer network. Systems such as Kazaa, eDonkey, Gnutella, Direct Connect, etc. are examples of peer-to-peer networks. In most of these networks, Internet users trade files by directly connecting one-to-one. The advantage of this method is that files can be shared without having access to a server, and because of this there is little accountability for the contents of the files. Hence, these networks tend to be very popular for illicit files such as music, movies, pirated software, etc. Typically, a downloader receives a file from a single source, however some clients allow downloading a single file from multiple sources for higher speeds.
BitTorrent is a protocol designed for transferring files. It is peer-to-peer in nature, as users connect to each other directly to send and receive portions of the file. However, there is a central server (called a tracker) which coordinates the action of all such peers. The tracker manages connections, but does not have any knowledge of the contents of the files being distributed, and therefore a large number of users can be supported with relatively limited tracker bandwidth. The key philosophy of BitTorrent is that users should upload (transmit outbound) at the same time they are downloading (receiving inbound.) In this manner, network bandwidth is utilized as efficiently as possible. BitTorrent is designed to work better as the number of people interested in a certain file increases, in contrast to other file transfer protocols.